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The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated., (© 2015, The International Biometric Society.)

In clinical development, an adaptive design combining results from two separate studies (e.g., a seamless adaptive design with a dose finding study phase and a confirmatory study phase) is commonly considered. The purpose of an adaptive design is not only to reduce lead time between the two studies, but also to evaluate the treatment effect in a more efficient way. In this paper, the focus is on the case where the study objectives are the same but the time durations of the study periods are different in the two stages. In particular, event data are collected in both stages. Statistical procedure for combining data observed from the two different stages is discussed. Furthermore, results on hypotheses testing and sample size calculation are derived for the comparison of two treatments.

To compare the survival functions based on right-truncated data, Lagakos et al. proposed a weighted logrank test based on a reverse time scale. This is in contrast to Bilker and Wang, who suggested a semi-parametric version of the Mann-Whitney test by assuming that the distribution of truncation times is known or can be estimated parametrically. The approach of Lagakos et al. is simple and elegant, but the weight function in their method depends on the underlying cumulative hazard functions even under proportional hazards models. On the other hand, a semi-parametric test may have better efficiency, but it may be sensitive to misspecification of the distribution of truncation times. Therefore, this paper proposes a non-parametric test statistic based on the integrated weighted difference between two estimated survival functions in forward time. The comparative results from a simulation study are presented and the implementation of these methods to a real data set is demonstrated., (Copyright 2006 John Wiley & Sons, Ltd.)

In clinical trials or drug development studies, researchers are often interested in identifying which treatments or dosages are more effective than the standard one. Recently, several multiple testing procedures based on weighted logrank tests have been proposed to compare several treatments with a control in a one-way layout where survival data are subject to random right-censorship. However, weighted logrank tests are based on ranks, and these tests might not be sensitive to the magnitude of the difference in survival times against a specific alternative. Therefore, it is desirable to develop a more robust and powerful multiple testing procedure. This paper proposes multiple testing procedures based on two-sample weighted Kaplan-Meier statistics, each comparing an individual treatment with the control, to determine which treatments are more effective than the control. The comparative results from a simulation study are presented and the implementation of these methods to the prostate cancer clinical trial and the renal carcinoma tumour study are presented., (2004 John Wiley & Sons, Ltd.)